Analysis
Vibrational loading was restricted to the vertical direction with respect to the radiator installation (cross flow) and was applied in a gravitational manner varying from 1G to 15G’s.

Several assumptions were made in the analysis. The FEA model was of one tube restrained at approx. 14.5" intervals along its length to simulate the tube-to-tube weld joint at those points. For model simplification purposes, the external air fins were neglected. Loading in the fore/aft direction was deemed insignificant due to tube geometry and resulting comparative strength in that direction. Thermal and internal pressure loading were not part of this analysis.

To account for the mass of the coolant (density of water at 70° C) and air fins (not modeled), a stress and displacement multiplier was established. This was developed by calculating an equivalent material density (see hand-calculations) which was applied to the FEA model as a material property providing the results.

All computer modeling and FEA was performed using SolidWorks 99 and Cosmos/Works V5, build 1999/197.

Results & Conclusions
The calculated maximum stress and deflection of each load scenario, 1G, 5G, 10G, and 15G, are shown on the attached plots. The relationship between G-load and stress and the relationship between G-load and deflection are linear as expected. Therefore stress and deflection can be predicted for any G-load as long as the resulting stresses are in the elastic range of Aluminum.

The "Coolant and Air Fin Mass Multiplier" was determined to be 1.511.

The radiator tube material, 6063-T6 Aluminum, properties are as follows:

• Yield Tensile Strength = 31,000 psi
• Ultimate Tensile Strength = 35,000 psi
• Endurance Limit = 10,000 psi

The Endurance Limit of 10,000 psi is based on a fatigue life of 500,000,000 cycles, which is a common "design-life" used for Aluminum components. (Mechanical properties furnished by "Ryerson Stock List" catalog.) The following example explains what this 500 million cycle life means.

If the radiator were installed in a vehicle which input loads at 12 cycles/second which resulted in a peak alternating stress of 10,000 psi in the tube, at an average run-time speed of 30 mph, the tube could be expected to live 347,222 miles (500 million cycles).

At 15G’s a maximum stress of 785 psi (519 psi x 1.511 water mass factor) was calculated. This is far below the endurance limit of the material and therefore will not produce a failure within 500 million cycles.

Recommendations
Based on this analysis, tube failure due to vibrational loading is not an issue. The .785 ksi stress level is so low that it doesn’t show up on published fatigue life S-N curves for Aluminum materials.

Sincerely,

Brian Merklein
Mechanical Engineer
Schmidt Engineering, Inc.
4466 Hwy. P - Suite 204
Jackson, WI 53037
Phone: 262-677-1221
Fax: 262-677-1224
Email: info@schmidtengineering.com